Essential Mods: Adaptation/[Rolling Guard], [Redirection], and Blazing Pillage. Everything else is extra

With modding as Hildryn your priority goes Strength>Duration>Range>Efficiency

• Strength is key to increase your shielding returns, the amount of shields you give, armor strip, and the slow from Gloom
• Duration is to negate the drain you'll obtain from the constant uptime of Haven and Gloom, and how far your Pillage goes
• Range increases initial radius on 2, and the radius on Gloom and Haven, very nice but not necessary
• Efficiency is typically a dump stat as though it helps with initial drain Duration, Pillage and arcane aegis negates any problems you might have with your shields
• Growing Power helps with getting more slow/armor strip if you have a primer like Cedo or Kuva Nukor
• Blazing Pillage is essential because it allows you to get more shields, more armor stripping, and status procs for CO melee
• Molt Augmented is now the best Arcane to put on [Hildryn] as it allows you to have even more Strength and gives you the potential to use Narrow Minded in your build for more range, asides from that Molt Efficiency or Arcane Aegis/Barrier are your best Secondary Arcane options.
• [Hildryn] badly needs a subsumed ability as their 4 is next to useless, and in the times where it is useful you'd be better off with a Gara or Limbo or Khora
• Other subsumed abilities that would be good for [Hildryn] is Electric Elemental Ward for more shielding to yourself and allies and being able to CC anyone who shoots you (plus the passive dmg) or Breach Surge which is good for the blind and increased dmg
• Personally Gloom is my favourite as it keeps the Ability Strength increase from Growing Power indefinitely along with 3 so you just have to worry about using your 2

UPDATES

1ST UPDATE:

I've tested this build a lot in low and high level missions. In high level where you're moving around a lot you'll want [Natural Talent] to decrease down time and to be able to cast your 2 faster, and use [Rolling Guard] for after your shields are down. In lower levels though its better to use adaptation, stretch and streamline as the enemies won't be surviving as long and your armor/shield gain wont be as high.

2ND UPDATE:

With the introduction of the Angels of Zariman, Hildryn got 3 really good arcanes.

• Molt Augmented, which increases [Hildryn]'s max Strength to a Ludicrous 383%, which allows you to take Overextended and not take any huge penalties as a Result, while increases your range by a lot.
• Molt Efficiency, increases [Hildryn]'s Duration as long as her shields are active. Very nice but not necessary, however if you're going for something like gloom or another Crowd Control Ability you won't get hit as much to be able to effectively utilize Arcane Aegis and Arcane Barrier, if you aren't however you may want to still use one of them in one slot and Molt Augmented in the other.
• Finally Cascadia Overcharge which gives your secondary an additional 300% Crit Chance. Almost every meta secondary apart from primaries need crit chance like people need water, and since with Pillage you're going to constantly have Overshields it will constantly be active.

3RD UPDATE:

With the introduction of Veilbreaker it might not seem like it's necessary to have all this Ability Strength as the Armor Strip Changes made having a lot of armor strip in one cast not as needed, especially since you would cap out on Glooms slow with a lot less strength. With the new changes you can just cast twice with 50% armor strip and achieve roughly the same result, especially with a mod like [Natural Talent] it makes Strength a lot less desirable.

However personally I prefer the higher Strength as I'll be able to one shot most things I would ever face with my balefire, I'll only have to use Pillage once to remove 96% armor which is enough Armor Strip to take care of most enemies aside from maybe levels 3000+, my [Blazing Pillage] damage would also be increased, because of these factors my build will stay the same, but you're welcome to swap some strength for some more range/utility options.